Conspiracy theories concerning the fate of former Nazi German leaders are 10 a pfennig. Did Martin Bormann, Hitler's secretary, live to a ripe old age somewhere in South America? Are we sure it was the Führer's corpse that was burned by aides in the courtyard of the Reich Chancellory as the Red Army stormed Berlin in May 1945? And what about Himmler? Is it just possible that the scrawny middle-aged man in glasses who committed suicide at the British camp at Luneburg after capture that same month was in fact a stand-in for the feared SS Reichsführer? That Himmler himself - who as late as May 5 had claimed that he, for one, "would never commit suicide" - had somehow slipped out of the Fatherland and set out on some not-so-vainglorious quest to set up a secret Fourth Reich?

Well, maybe. Possibly. Perhaps. Anything is possible, after all, in the breathless aftermath of world war. Certain physical details of the dead man at Lüneburg do seem different from Himmler's: you can see them in the studious photos reproduced in this book. One nostril is larger than the other, whereas Himmler's were symmetrical. The corpse doesn't appear to sport a duelling scar, which means that unless the dead man was wearing make-up (popular among senior Nazis), he wasn't the son born to Anna and Dr Gebhard Himmler on October 7 1900.

Hugh Thomas is "a surgeon and forensic expert of international repute", says the blurb to this dense, fascinating yet ultimately bothersome book. "His first book, The Murder of Rudolf Hess , caused a worldwide furore. His second, Hess: A Tale of Two Murders , precipitated a six-month Scotland Yard inquiry that saw its report immediately suppressed." Thomas does have a scalpel-sharp eye for detail - as you would hope of a man of his profession. He also writes well when he allows himself to get beyond the weight of the obsessive detail that bogs parts of this book down like one of Panzer General Guderian's tanks attempting to advance on Moscow in December 1941. It was Guderian who commented that Himmler was "a man from another planet".

The central thesis of Thomas's book - and the evidence for it is vivid - is that Himmler was attempting to set up a Fourth Reich outside the boundaries of Hitler's Germany. Quite aware that Germany had effectively lost the war as early as 1943, Thomas's Himmler set about channelling the Croesan riches amassed by the SS and pro-Nazi German finance and industry into Swiss and South American bank accounts. An FBI/OSS report of November 1944, written by Senator Harley M Kilgore and backed by the US Treasury and State departments, noted: "The German aggressors have begun to pursue the strategy which they found successful a quarter of a century ago. They are already deploying their economic wares throughout the world in preparation for a third attempt at world domination." Which, of course, appeared to happen from the 1950s, when the Federal Republic's "economic miracle" astounded the nations that had borne the brunt of the fighting against Hitler, Himmler and the rest of their vile crew.

Thomas piles up a massively detailed case suggesting that Nazi money exported to safe financial havens in the late stages of the second world war was, to a previously underplayed extent, responsible for Germany's rise to economic power in the decade following Hitler's downfall. Well, maybe. Perhaps. Possibly. To his credit, Thomas uses these defusing words frequently in a book that might otherwise overstretch the imagination and, in turn, credit Himmler with too much intelligence and insight.

His portrait of Himmler is, in fact, the best part of SS-1 , which suffers from being three books in one. There's an excellent mini-biography of Himmler, a Byzantine analysis of the links between Nazi and international finance during the war, and a forensic examination of the corpse that may or may not have been that of the Reichsführer.

The description of Himmler's childhood and youth is compelling. This "man of quiet, unemotional gestures, a man without words" was fastidious and possessed of a phenomenal memory; he kept a daily diary recording everything that happened to him. He put these skills to chilling use when he began to wipe out Europe's Jews and gypsies, communists and homosexuals. Everything the SS did was planned and recorded fastidiously. No one escaped the Reichsführer's eyes, beady behind those infamous rimless glasses. Everyone needed to be watched, especially Paula Stolzle, his elder brother's pretty and flirtatious fiancée. Disapproving of sexy women, shortly before he joined the Nazi party the puritanical young Himmler employed a private detective to follow Stolzle; he made the couple's lives so fraught that the engagement was called off.

Himmler went on to become a lot creepier and a lot more dangerous, although he did marry, losing his virginity at the age of 28 to a nurse seven years his senior who thought those rimless glasses - she persuaded him to wear them - rather fetching. It's just this sort of near-forensic detail that makes Thomas's book worthwhile. Quick as a blitzkrieg, this bloodless young man is Reichsführer SS (in 1929, aged 28). The title SS-1 refers to Himmler's position as head of the Schutz Staffel; it was also the licence plate of his BMW staff car. According to Josef Goebbels, "except for Hitler, no one is entirely without fear of Himmler".

No one? German business certainly appears to have gone along with him. So too did business interests in Washington, London and Zurich. If there had been some shady Allied agreement to allow Himmler to escape the wrath of the Nuremberg trials and set up shop elsewhere while pretending that he had committed suicide, then it had surely been abandoned by May 1945. Himmler, the SS and German big business may well have been in cahoots with elements in Wall Street and the City of London; Britain's royal family, with its shareholding in German companies, was also that bit too close to him (Prince Christopher Mountbatten, says Thomas, was on Himmler's staff). Yet ultimately the SS Reichsführer was surely too ghastly to be acceptable to the international business and banking community.

It's true that the British dug up the corpse for reidentification, and it's true that several members of British intelligence, Kim Philby among them, were not immediately convinced that Himmler was dead. Yet if he weren't, we would surely have heard something about it by now. Wouldn't we?